Hi Emilia,
Which version of TELEMAC-2D are you using?
Before Thompson's theory was revisited by Jean-Michel (Hervouet) in version 6.1 (so that it can be used in parallel, please see the proceedings of the 18th TELEMAC-MASCARET User Club), there was a big difference for time computations if using Thompson or not (something like 8 times if I remember). In parallel with version 6.2, I have not noticed such differences (even though a little bit faster without Thompson's conditions).
In my proper experience, Thompson conditions work better if you have both elevation and velocities values.
When running simulations with only elevation without Thompson's conditions, I got results that are not so far from simulations with both elevation and velocities and with Thompson's conditions, except close to the open boundaries and some warning messages such as
'ILL-POSED PROBLEM, ENTERING FREE VELOCITY
FOR EXAMPLE AT BOUNDARY POINT NUMBER'
The problem occurs in particular when the current is directed inwards on the open boundary though prescribing elevation.
I would say that if you are far from the open boundary, your result is OK with classic boundary condition.
Perhaps Jean-Michel or someone else will be able to complete this answer.
Hope this helps,
Chi-Tuan
PS: if your area is covered by one local tidal solution provided by Oregon State University (e.g. European Shelf or Iceland)
volkov.oce.orst.edu/tides/region.html
perhaps, you can try to use the new developments of TELEMAC 6.2 to deal with these databases of harmonic constants? OSU provides both elevation and velocity values for open boundary conditions, so that Thompson's conditions can be used.